To do this, you will need a programme that will hook into the Save As Dialog of Solidworks and manipulate the behaviour. This is not a problem, but not as easy as it sounds. If the programme is for internal use, maybe AutoHotkey could be interesting. This scripting language allows you to do the hook easily. Unfortunately, there are interfaces in the EPDM API that cannot be accessed via scripts. So you need some more code in .NET. The combination of both makes it possible to do this task with a minimum of code.

I do not want to provide an out of the box solution, but I want to show what is possible with this scripting language. Maybe these possibilities will give some new ideas.